Question

PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=$4\sqrt{x}$ cm then the length of each side of the rhombus (in terms of ‘x’) is:

• A. $(\sqrt{x }+ 18) cm$
• B. $5\sqrt{x}\, cm$
• C. 18 cm
• D. 30 cm

Answer 1

Answer: (D)

30 cm

Answer 2

The correct option is (D): 30 cm.

According to the question,
PQ = 30 cm, PR = 36 cm and QS = $4\sqrt{x}$ cm
Therefore, OP = $\frac{36}{2}$ = 18 cm and OQ = $\frac{4\sqrt{x}}{2}$= $2\sqrt{x}$ cm (Since diagonals of rhombus bisect each other at right angle)
In triangle POQ, using Pythagoras theorem
182 + ($2\sqrt{x}$)2 = 302
Or, 324 + 4x = 900
Or, 4x = 576
Or, x = 144
Therefore, length of each side of the rhombus = $\sqrt{x}$+18=12+18=30 cm.